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Unformatted text preview: ENGRI 115 Engineering Applications of OR Fall 2007 The Maximum Flow Problem Homework 4 Due date: Thursday, October 4 in class. References: Lecture notes; Lab 4; Winston 8.3. The first two problems are practice problems, DO NOT hand them in. The TAs will be glad to help you if you have any questions. 1. Winston, page 430, Problem 4-5. 2. Winston, page 430, Problem 6. (Solution is sketched in Appendix 3 of the textbook! Make sure you understand why a maximum flow in the given network corresponds to a feasible delivery plan.) 3. Consider the following network, with two numbers on the arcs: the first is a proposed flow, and the second is the capacity of the arc. 1,2 1 6 s t 1,3 2,2 0,1 1,2 0,1 2,2 2,3 1,1 4 5 2 3 a. Is the indicated flow feasible? Explain. What is the value of the flow? c. Is the above flow optimal? If yes, show a cut that proves optimality of the flow. If not, improve the flow until optimality (and explain why your solution is optimal)....
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- Fall '05
- Flow network, Maximum flow problem, Max-flow min-cut theorem, maximum flow